526 UCB, Boulder CO 80309

Abstract

In this talk we discuss developments in a first-order system least squares (FOSLS) approach for the numerical approximation of the solution of the
equations of geometrically-nonlinear elasticity. We follow a Newton-FOSLS algorithm where each linear step is solved as a two-stage, first-order
system under a least squares finite element discretization. With appropriate regularity we show H^{1} equivalence of the quadratic part of the FOSLS
functional norm in the case of pure displacement boundary conditions. Results hold for deformations near the reference configuration, a set we show
to be largely coincident with the set of deformations allowed by the physical model. In this regime the discrete systems that result from using
standard finite element subspaces of H^{1} can be solved with optimal complexity. Numerical results are given for both pure displacement and mixed
boundary conditions and confirm optimal multigrid performance and finite element approximation properties.